[代码资源] 用对分法解超越方程

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发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

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范例：用对分法求方程在(0,1)内的根，要求误差不超过0.1；
求解程序如下：

clear;clc;close
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% n=input('请输入迭代次数：');
7 X1 ^) O; v# T8 e
% qujian=input('请输入初始区间：');% k6 l& R/ q+ L
n=100;
2 y' [$ E& H, w& F: e
wucha=0.005;8 J F7 y/ e4 u( Z$ b( {( g
qujian=[0 1];
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a(1)=qujian(1);
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b(1)=qujian(2); $ \% L/ l0 b0 L7 e# g O
a0=a(1);8 \2 O/ S4 w5 g( T\" W
b0=b(1);/ ^# @- q+ y2 |2 S6 @9 {
x=qujian;$ V/ W. \\" q: J\" D6 l# q5 \& R* S4 S
y=exp(x)+10*x-2;
d: w: f5 Z7 F. u4 Q
y1=y(1); %小于0
' X# i3 `\" P! q$ x! o6 a9 c: t. D
y2=y(2); %大于0
: M! X/ |8 y$ r) X: H( k
for i=1:n %总迭代次数
8 m/ G, B1 U7 s: v6 [7 k
c(i)=(a+b)/2;
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f(i)=exp(c(i))+10*(c(i))-2;
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kesai_k(i)=(b-a)/2;+ X6 B$ J7 @* b
if f(i)>0
P6 e5 E' b7 A# P9 R, g, c) s2 ^
b=c(i);* F: A2 w3 J\" R# p
b1(i)=c(i);
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a1(i)=a;
8 I! x! T+ \2 m; ?, j\" e
elseif f(i)<0
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a=c(i);) _: C d* w* D, w5 F3 a! T* G& u
a1(i)=c(i);) a; l8 c( q% o, N* Q% s\" Y4 x
b1(i)=b;5 d\" x9 M7 Q ^0 D0 t% z' g
elseif f(i)==0||kesai_k(i)<=wucha6 v0 W# s6 y. w1 I) Y. t4 @
disp('精确值解为：');3 c1 l0 Q# {8 m1 P X- H
disp(c(i));7 F1 Q7 m$ D' E+ I( n
break;
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end
3 `3 C k: r* j. I4 I/ O- B
end. f1 f, x' H) y( B
disp('迭代次数：');
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fprintf('%d次\n\n',n);
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fprintf('要求误差%f\n\n',wucha);& M2 H# i\" ~- `$ Z! w) h& v
disp('输出矩阵为：');% ]+ ~$ Y9 }' T8 ^ q
A=[a0 a1]';
7 Q3 r- [- b' l0 i\" J& c
B=[b0 b1]';: V8 A' r4 ~& _
format long. C h3 S2 q# d% S
data_out=[A B c' f' kesai_k']( N3 R% J2 | E) A1 D
xlswrite('二分法处理数据.xls',data_out);

复制代码

结果输出情况：

精确值解为：. [4 y2 P _+ E$ V- i( O( W
0.0905
/ h: v4 G6 M$ `% t( }
! e. B1 E6 j5 \
迭代次数：+ k6 y, U) l! `
100次. ]; w! O- G9 e* b( I0 I% u, J. ?
, z) K% |/ Z% j& m! A5 }% y( y' ?
要求误差0.005000
) v( V- j7 E1 o* T2 S% N1 c! Z; S
; p9 K2 B+ c& _3 E\" Z
输出矩阵为：
. E7 S7 ?6 t1 R0 E+ C
% M; X. t0 }6 _, l0 Q
data_out =* K7 Q6 `9 Q8 } W: y1 Y
3 D! k, ] j1 S1 v
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000# `# D: ]# ]* I9 U$ V: \
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
5 ~3 ]$ n/ Q( ~2 y& v
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
3 t8 o. W5 b) K; c# P! F
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.0625000000000008 g5 k2 a4 B5 e$ O7 G& g
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
- {' _ ~: [& E9 k\" w
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.0156250000000005 ?\" I @9 C# L( ?
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
6 }\" ?/ F4 O& Q
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
/ @\" i# l/ Z$ w: b- ?5 Z+ T
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
: F$ |8 n: g* r3 j. N8 U4 e: Y
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
; G5 E5 P4 ?, n9 w8 ~2 M9 Y- e0 W( D
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000* _; x8 S; e+ C% s7 F
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.0002441406250009 r2 I- [9 O X7 E3 ]$ i- p
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500: N( ^9 Y0 c6 K; @
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
8 Q/ g- _9 ^0 U% a, L
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
0 R2 o8 {4 b+ q- F7 ^$ m7 e
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890636 S7 C1 _; Y4 Y
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531\" j3 _+ ~$ ]+ J5 j, W/ |\" x5 q
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
1 d5 ]3 Q7 g/ Q
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633; O1 F+ x& w+ W5 `$ [! c
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316$ B/ c L0 \9 q4 j% l0 Y
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158 j8 V. n0 T$ c4 E
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185790 p: Y' M* S7 r, O# @
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
6 J; M/ x2 p4 Y; r3 g# B
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
2 n7 w% S; L4 u% W. U7 k% H
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322\" M2 ^! K4 q! r9 s$ {, D7 m
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161' q0 X# [/ E) I
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
& }# \% g: S9 T. ]* s. E' V9 \. K
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
+ m8 H9 c* E7 H C& F
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645/ ~+ m/ C' j' {# F. |7 A
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.0000000009313234 w, q' l8 E/ p0 G5 [\" J
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.0000000004656617 }4 [! K# `; M9 A
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328315 X/ E, {2 g4 ?4 \+ @
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
+ z/ z9 J m9 y/ [# ~/ j
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
3 {\" W O( V$ \6 h; M
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104! P\" r& E2 E0 x0 U# ?0 y# B
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552/ a3 T$ w9 w: A/ W# s
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
\" J3 d' H3 m\" v$ `- l# s7 {
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
5 b1 D5 t2 k3 K8 T( _\" t
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
+ v7 E\" i% ?! n
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009090 H3 c. Z# Y# s8 s, l
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
9 |/ @5 Y+ h7 K. H, p2 D2 Y
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227\" @+ _+ [8 [5 t/ G! g7 ~& }
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
! T' ?$ G* C6 d* H% u
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057& }3 b9 D: `3 V5 q6 W/ {0 x
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028% N& o0 \- Y0 I
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.0000000000000146 b; f, C' k% a\" m9 S% n
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
& _6 _2 O% d3 u$ A2 X* i0 E% k& P
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000047 U- T4 k\" r0 l9 z1 w# f1 t, H! s U) w
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
6 N9 W# d* ?' W, Q( ^
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
8 V3 D& g% [0 e' t+ u- } ]) e8 a
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000